# 2024-09-30

This following is a very brief summary of what happened in class on 2024-09-30.

We introduced the notion of a map between categories, called a functor. Each functor consists of two functions, one map for the objects and one map for the arrows. These two functions must "respect the categorical structure", which basically means they commute with composition and send identity arrows to identity arrows. We then spent the majority of our time looking at a few examples, namely:

- The power set functor
- Some forgetful functors
- The abelianization functor

In our next class we will look at more examples!

## Concepts

## References

- Mac Lane: Pages 13-15